Talk:Normal forms: Difference between revisions

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:: Oh, no big deal at all. Thanks for updating the page. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:17, 24 June 2021 (UTC)

== ~~how~~ best to handle the new canonical form for RTT matrices w/r/t normal form ==

== How best to handle the new canonical form for RTT matrices w/r/t normal form ==

I recently published [[Canonical form|a page on the xen wiki proposing a canonical form for RTT mappings (or comma-bases)]]. This new page of mine solves a problem that this page seems to have set out to solve but not finished the job: establishing a form for RTT matrices which ''uniquely identifies them'', for a definition of uniqueness that is appropriate to the RTT domain. And so my page refers to this page in several places, mostly critiquing it.

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:::: Re: the new "Tenney minimal" section. I think it's an interesting idea to present a comma list in a different normal form than HNF (or defactored + HNF = canonical form), namely, some definition of the simplest possible ratios. However, I have several questions.

# You state that this is already the case that temperament pages use this form. I have no reason to believe they're not. But I didn't know that was the case. How do you know this?

# Do you have a definition for this normal form somewhere? If you don't yet, I would recommend excluding it from this page until it's better developed. I can easily see how the product complexity of ratios can be easily calculated individually, but minimizing the simplicity of multiple ratios may be somewhat subtle.

::::# You state that this is already the case that temperament pages use this form. I have no reason to believe they're not. But I didn't know that was the case. How do you know this?

# Why name it "Tenney minimal"? I do not see that this term has wide use on the wiki or Discord already. It seems like an unnecessary eponym. If it is related to the Tenney height of the ratios, wouldn't it be equivalent and simpler to just refer to their product complexity?

::::# Do you have a definition for this normal form somewhere? If you don't yet, I would recommend excluding it from this page until it's better developed. I can easily see how the product complexity of ratios can be easily calculated individually, but minimizing the simplicity of multiple ratios may be somewhat subtle.

::::# Why name it "Tenney minimal"? I do not see that this term has wide use on the wiki or Discord already. It seems like an unnecessary eponym. If it is related to the Tenney height of the ratios, wouldn't it be equivalent and simpler to just refer to their product complexity?

:::: That's all for now. Thanks for helping with this. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:54, 29 September 2021 (UTC)

:::: I would also like to see across the wiki places where "normal list", "normal comma list", "normal interval list", "normal val list", "normal list basis", etc. standardized to "canonical mapping" or "canonical comma-basis", linking here. What do you think? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:54, 29 September 2021 (UTC)

::::: Sounds like a lot of work to be done!

::::: Re: the beep example. We've adopted an additional step for positive generator in Hermite normal form. Analogously, we can add one to flip the monzo if it turns out negative. So [{{monzo| 0 3 -2 0 }}, {{monzo| 2 2 -1 -1 }}] instead.

::::: Re: rename and standardization. I don't think renaming this page and/or "standardize" the terms in other pages is a priority. Until some data from other users are collected, I can't exclude that what we project as standardization may actually be prescriptivism.

::::: Re: Tenney minimal. 1. By examining some comma lists. For septimal meantone, the normal form would be {81/80, 59049/57344}. Yet the comma list shown in the temp page is {81/80, 126/125}. 2. I've worked out a lot of comma bases and haven't encountered a single example where the definition shown in this page leads to ambiguous results. Now I definitely can't assert there's no exceptions, I'm afraid it'd better be there since all the comma bases shown in the temp pages need an explanation. 3. It's attested in the ''Genesisplus'' page. We can call it ''ratio-product simplest form'', but that's longer and still needs explanation. You know, you can also remove ''Benedetti height'' in favor of ''ratio-product'', and remove ''Tenney height'' in favor of ''logarithm of ratio-product''. I just don't think that's how human language works. Benedetti height is one of many types of heights. In the topic of heights, each type is equally distinct despite one of them being simpler in formula, so each type equally deserves a name. From there is derived ''Tenney-minimal'' as one of many possible minimal forms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 23:55, 29 September 2021 (UTC)

@@ Line 9: / Line 9: @@
 :: Oh, no big deal at all. Thanks for updating the page. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 15:17, 24 June 2021 (UTC)
-== how best to handle the new canonical form for RTT matrices w/r/t normal form ==
+== How best to handle the new canonical form for RTT matrices w/r/t normal form ==
 I recently published [[Canonical form|a page on the xen wiki proposing a canonical form for RTT mappings (or comma-bases)]]. This new page of mine solves a problem that this page seems to have set out to solve but not finished the job: establishing a form for RTT matrices which ''uniquely identifies them'', for a definition of uniqueness that is appropriate to the RTT domain. And so my page refers to this page in several places, mostly critiquing it.
@@ Line 58: / Line 58: @@
 :::: Re: the new "Tenney minimal" section. I think it's an interesting idea to present a comma list in a different normal form than HNF (or defactored + HNF = canonical form), namely, some definition of the simplest possible ratios. However, I have several questions.
-# You state that this is already the case that temperament pages use this form. I have no reason to believe they're not. But I didn't know that was the case. How do you know this?
-# Do you have a definition for this normal form somewhere? If you don't yet, I would recommend excluding it from this page until it's better developed. I can easily see how the product complexity of ratios can be easily calculated individually, but minimizing the simplicity of multiple ratios may be somewhat subtle.
+::::# You state that this is already the case that temperament pages use this form. I have no reason to believe they're not. But I didn't know that was the case. How do you know this?
-# Why name it "Tenney minimal"? I do not see that this term has wide use on the wiki or Discord already. It seems like an unnecessary eponym. If it is related to the Tenney height of the ratios, wouldn't it be equivalent and simpler to just refer to their product complexity?
+::::# Do you have a definition for this normal form somewhere? If you don't yet, I would recommend excluding it from this page until it's better developed. I can easily see how the product complexity of ratios can be easily calculated individually, but minimizing the simplicity of multiple ratios may be somewhat subtle.
+::::# Why name it "Tenney minimal"? I do not see that this term has wide use on the wiki or Discord already. It seems like an unnecessary eponym. If it is related to the Tenney height of the ratios, wouldn't it be equivalent and simpler to just refer to their product complexity?
 :::: That's all for now. Thanks for helping with this. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:54, 29 September 2021 (UTC)
 :::: I would also like to see across the wiki places where "normal list", "normal comma list", "normal interval list", "normal val list", "normal list basis", etc. standardized to "canonical mapping" or "canonical comma-basis", linking here. What do you think? --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:54, 29 September 2021 (UTC)
+::::: Sounds like a lot of work to be done!
+::::: Re: the beep example. We've adopted an additional step for positive generator in Hermite normal form. Analogously, we can add one to flip the monzo if it turns out negative. So [{{monzo| 0 3 -2 0 }}, {{monzo| 2 2 -1 -1 }}] instead.
+::::: Re: rename and standardization. I don't think renaming this page and/or "standardize" the terms in other pages is a priority. Until some data from other users are collected, I can't exclude that what we project as standardization may actually be prescriptivism.
+::::: Re: Tenney minimal. 1. By examining some comma lists. For septimal meantone, the normal form would be {81/80, 59049/57344}. Yet the comma list shown in the temp page is {81/80, 126/125}. 2. I've worked out a lot of comma bases and haven't encountered a single example where the definition shown in this page leads to ambiguous results. Now I definitely can't assert there's no exceptions, I'm afraid it'd better be there since all the comma bases shown in the temp pages need an explanation. 3. It's attested in the ''Genesisplus'' page. We can call it ''ratio-product simplest form'', but that's longer and still needs explanation. You know, you can also remove ''Benedetti height'' in favor of ''ratio-product'', and remove ''Tenney height'' in favor of ''logarithm of ratio-product''. I just don't think that's how human language works. Benedetti height is one of many types of heights. In the topic of heights, each type is equally distinct despite one of them being simpler in formula, so each type equally deserves a name. From there is derived ''Tenney-minimal'' as one of many possible minimal forms. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 23:55, 29 September 2021 (UTC)